The weakly screened electron-hole interactions in an atomically thin semiconductor not only downshift its excitation spectrum from a quasiparticle one, but also redistribute excitation energies and wave-function characters with profound effects on the diverse modes of the material response, including the exciton-phonon scattering processes accessible to resonant Raman measurements. Here, we develop a first-principles framework to calculate frequency-dependent resonant Raman intensities that includes excitonic effects and goes beyond the Placzek approximation. We show how excitonic effects in ${\mathrm{MoS}}_2$ strongly regulate Raman scattering amplitudes and thereby explain the puzzling near absence of a resonant Raman response around the $A$ and $B$ excitons (band-edge excitations which produce very strong signals in optical absorption), and also the pronounced strength of the resonant Raman response from the $C$ exciton (a higher-energy excitation arising from parallel valence and conduction bands). Furthermore, this efficient perturbative approach reduces the number of $GW$ plus Bethe-Salpeter-equation calculations from two per Raman mode (in finite displacement) to one for all modes and affords a natural extension to higher-order resonant Raman processes.

• Received 13 July 2018
• Revised 25 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.161405